A259395 - OEIS

%I #11 Sep 08 2022 08:46:13

%S 0,0,15228,705024,1885680,-66355200,-792382500,-4986842112,

%T -22516232256,-81696522240,-252908835300,-693126720000,-1723987588752,

%U -3961019252736,-8517765880260,-17315965900800,-33541737120000,-62298041352192,-111515651966916,-193198552634880

%N a(n) = -3*n^2*(n-1)^4*(n+1)*(11*n^3+49*n^2-439*n+171).

%H M. P. Delest, <a href="http://dx.doi.org/10.1016/0097-3165(88)90071-4">Generating functions for column-convex polyominoes</a>, J. Combin. Theory Ser. A 48 (1988), no. 1, pp. 12-31. See expression D in Theorem 16 page 29.

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

%F G.f.: 324*x^2*(47+1659*x - 15531*x^2 - 156895*x^3 - 216255*x^4 - 17547*x^5 + 31451*x^6 + 3471*x^7) / (1-x)^11.

%F a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11).

%p A259395:=n->-3*n^2*(n-1)^4*(n+1)*(11*n^3+49*n^2-439*n+171): seq(A259395(n), n=0..25); # _Wesley Ivan Hurt_, Jun 29 2015

%t Table[-3 n^2 (n - 1)^4 (n + 1) (11 n^3 + 49 n^2 - 439 n + 171), {n, 0, 23}]

%o (Magma) [-3*n^2*(n-1)^4*(n+1)*(11*n^3+49*n^2-439*n+171): n in [0..20]];

%Y Cf. A001105, A005435, A259364.

%K sign,easy

%O 0,3

%A _Vincenzo Librandi_, Jun 26 2015